TSTP Solution File: SET592+3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Jul 27 13:13:46 EDT 2022

% Result   : Theorem 1.76s 1.93s
% Output   : Refutation 1.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   10 (   8 unt;   0 nHn;  10 RR)
%            Number of literals    :   13 (   5 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    4 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ subset(A,empty_set)
    | A = empty_set ),
    file('SET592+3.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ subset(A,B)
    | ~ subset(A,C)
    | subset(A,intersection(B,C)) ),
    file('SET592+3.p',unknown),
    [] ).

cnf(16,axiom,
    dollar_c3 != empty_set,
    file('SET592+3.p',unknown),
    [] ).

cnf(17,plain,
    empty_set != dollar_c3,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),
    [iquote('copy,16,flip.1')] ).

cnf(28,axiom,
    subset(dollar_c3,dollar_c2),
    file('SET592+3.p',unknown),
    [] ).

cnf(29,axiom,
    subset(dollar_c3,dollar_c1),
    file('SET592+3.p',unknown),
    [] ).

cnf(31,axiom,
    intersection(dollar_c2,dollar_c1) = empty_set,
    file('SET592+3.p',unknown),
    [] ).

cnf(43,plain,
    subset(dollar_c3,empty_set),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[29,2,28]),31]),
    [iquote('hyper,29,2,28,demod,31')] ).

cnf(59,plain,
    empty_set = dollar_c3,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[43,1])]),
    [iquote('hyper,43,1,flip.1')] ).

cnf(61,plain,
    $false,
    inference(binary,[status(thm)],[59,17]),
    [iquote('binary,59.1,17.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 10:46:49 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.76/1.93  ----- Otter 3.3f, August 2004 -----
% 1.76/1.93  The process was started by sandbox on n028.cluster.edu,
% 1.76/1.93  Wed Jul 27 10:46:49 2022
% 1.76/1.93  The command was "./otter".  The process ID is 4623.
% 1.76/1.93  
% 1.76/1.93  set(prolog_style_variables).
% 1.76/1.93  set(auto).
% 1.76/1.93     dependent: set(auto1).
% 1.76/1.93     dependent: set(process_input).
% 1.76/1.93     dependent: clear(print_kept).
% 1.76/1.93     dependent: clear(print_new_demod).
% 1.76/1.93     dependent: clear(print_back_demod).
% 1.76/1.93     dependent: clear(print_back_sub).
% 1.76/1.93     dependent: set(control_memory).
% 1.76/1.93     dependent: assign(max_mem, 12000).
% 1.76/1.93     dependent: assign(pick_given_ratio, 4).
% 1.76/1.93     dependent: assign(stats_level, 1).
% 1.76/1.93     dependent: assign(max_seconds, 10800).
% 1.76/1.93  clear(print_given).
% 1.76/1.93  
% 1.76/1.93  formula_list(usable).
% 1.76/1.93  all A (A=A).
% 1.76/1.93  all B (subset(B,empty_set)->B=empty_set).
% 1.76/1.93  all B C D (subset(B,C)&subset(B,D)->subset(B,intersection(C,D))).
% 1.76/1.93  all B (-member(B,empty_set)).
% 1.76/1.93  all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.76/1.93  all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.76/1.93  all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.76/1.93  all B C (intersection(B,C)=intersection(C,B)).
% 1.76/1.93  all B subset(B,B).
% 1.76/1.93  all B (empty(B)<-> (all C (-member(C,B)))).
% 1.76/1.93  all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.76/1.93  -(all B C D (subset(B,C)&subset(B,D)&intersection(C,D)=empty_set->B=empty_set)).
% 1.76/1.93  end_of_list.
% 1.76/1.93  
% 1.76/1.93  -------> usable clausifies to:
% 1.76/1.93  
% 1.76/1.93  list(usable).
% 1.76/1.93  0 [] A=A.
% 1.76/1.93  0 [] -subset(B,empty_set)|B=empty_set.
% 1.76/1.93  0 [] -subset(B,C)| -subset(B,D)|subset(B,intersection(C,D)).
% 1.76/1.93  0 [] -member(B,empty_set).
% 1.76/1.93  0 [] -member(D,intersection(B,C))|member(D,B).
% 1.76/1.93  0 [] -member(D,intersection(B,C))|member(D,C).
% 1.76/1.93  0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.76/1.93  0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.76/1.93  0 [] subset(B,C)|member($f1(B,C),B).
% 1.76/1.93  0 [] subset(B,C)| -member($f1(B,C),C).
% 1.76/1.93  0 [] B!=C|subset(B,C).
% 1.76/1.93  0 [] B!=C|subset(C,B).
% 1.76/1.93  0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.76/1.93  0 [] intersection(B,C)=intersection(C,B).
% 1.76/1.93  0 [] subset(B,B).
% 1.76/1.93  0 [] -empty(B)| -member(C,B).
% 1.76/1.93  0 [] empty(B)|member($f2(B),B).
% 1.76/1.93  0 [] B!=C| -member(D,B)|member(D,C).
% 1.76/1.93  0 [] B!=C|member(D,B)| -member(D,C).
% 1.76/1.93  0 [] B=C|member($f3(B,C),B)|member($f3(B,C),C).
% 1.76/1.93  0 [] B=C| -member($f3(B,C),B)| -member($f3(B,C),C).
% 1.76/1.93  0 [] subset($c3,$c2).
% 1.76/1.93  0 [] subset($c3,$c1).
% 1.76/1.93  0 [] intersection($c2,$c1)=empty_set.
% 1.76/1.93  0 [] $c3!=empty_set.
% 1.76/1.93  end_of_list.
% 1.76/1.93  
% 1.76/1.93  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.76/1.93  
% 1.76/1.93  This ia a non-Horn set with equality.  The strategy will be
% 1.76/1.93  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.76/1.93  deletion, with positive clauses in sos and nonpositive
% 1.76/1.93  clauses in usable.
% 1.76/1.93  
% 1.76/1.93     dependent: set(knuth_bendix).
% 1.76/1.93     dependent: set(anl_eq).
% 1.76/1.93     dependent: set(para_from).
% 1.76/1.93     dependent: set(para_into).
% 1.76/1.93     dependent: clear(para_from_right).
% 1.76/1.93     dependent: clear(para_into_right).
% 1.76/1.93     dependent: set(para_from_vars).
% 1.76/1.93     dependent: set(eq_units_both_ways).
% 1.76/1.93     dependent: set(dynamic_demod_all).
% 1.76/1.93     dependent: set(dynamic_demod).
% 1.76/1.93     dependent: set(order_eq).
% 1.76/1.93     dependent: set(back_demod).
% 1.76/1.93     dependent: set(lrpo).
% 1.76/1.93     dependent: set(hyper_res).
% 1.76/1.93     dependent: set(unit_deletion).
% 1.76/1.93     dependent: set(factor).
% 1.76/1.93  
% 1.76/1.93  ------------> process usable:
% 1.76/1.93  ** KEPT (pick-wt=6): 1 [] -subset(A,empty_set)|A=empty_set.
% 1.76/1.93  ** KEPT (pick-wt=11): 2 [] -subset(A,B)| -subset(A,C)|subset(A,intersection(B,C)).
% 1.76/1.93  ** KEPT (pick-wt=3): 3 [] -member(A,empty_set).
% 1.76/1.93  ** KEPT (pick-wt=8): 4 [] -member(A,intersection(B,C))|member(A,B).
% 1.76/1.93  ** KEPT (pick-wt=8): 5 [] -member(A,intersection(B,C))|member(A,C).
% 1.76/1.93  ** KEPT (pick-wt=11): 6 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.76/1.93  ** KEPT (pick-wt=9): 7 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.76/1.93  ** KEPT (pick-wt=8): 8 [] subset(A,B)| -member($f1(A,B),B).
% 1.76/1.93  ** KEPT (pick-wt=6): 9 [] A!=B|subset(A,B).
% 1.76/1.93  ** KEPT (pick-wt=6): 10 [] A!=B|subset(B,A).
% 1.76/1.93  ** KEPT (pick-wt=9): 11 [] A=B| -subset(A,B)| -subset(B,A).
% 1.76/1.93  ** KEPT (pick-wt=5): 12 [] -empty(A)| -member(B,A).
% 1.76/1.93  ** KEPT (pick-wt=9): 13 [] A!=B| -member(C,A)|member(C,B).
% 1.76/1.93  ** KEPT (pick-wt=9): 14 [] A!=B|member(C,A)| -member(C,B).
% 1.76/1.93  ** KEPT (pick-wt=13): 15 [] A=B| -member($f3(A,B),A)| -member($f3(A,B),B).
% 1.76/1.93  ** KEPT (pick-wt=3): 17 [copy,16,flip.1] empty_set!=$c3.
% 1.76/1.93  
% 1.76/1.93  ------------> process sos:
% 1.76/1.93  ** KEPT (pick-wt=3): 22 [] A=A.
% 1.76/1.93  ** KEPT (pick-wt=8): 23 [] subset(A,B)|member($f1(A,B),A).
% 1.76/1.93  ** KEPT (pick-wt=7): 24 [] intersection(A,B)=intersection(B,A).
% 1.76/1.93  ** KEPT (pick-wt=3): 25 [] subset(A,A).
% 1.76/1.93  ** KEPT (pick-wt=6): 26 [] empty(A)|member($f2(A),A).
% 1.76/1.93  ** KEPT (pick-wt=13): 27 [] A=B|member($f3(A,B),A)|member($f3(A,B),B).
% 1.76/1.93  ** KEPT (pick-wt=3): 28 [] subset($c3,$c2).
% 1.76/1.93  ** KEPT (pick-wt=3): 29 [] subset($c3,$c1).
% 1.76/1.93  ** KEPT (pick-wt=5): 30 [] intersection($c2,$c1)=empty_set.
% 1.76/1.93  ---> New Demodulator: 31 [new_demod,30] intersection($c2,$c1)=empty_set.
% 1.76/1.93    Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 1.76/1.93  22 back subsumes 21.
% 1.76/1.93  22 back subsumes 20.
% 1.76/1.93    Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] intersection(A,B)=intersection(B,A).
% 1.76/1.93  >>>> Starting back demodulation with 31.
% 1.76/1.93  
% 1.76/1.93  ======= end of input processing =======
% 1.76/1.93  
% 1.76/1.93  =========== start of search ===========
% 1.76/1.93  
% 1.76/1.93  -------- PROOF -------- 
% 1.76/1.93  
% 1.76/1.93  ----> UNIT CONFLICT at   0.00 sec ----> 61 [binary,59.1,17.1] $F.
% 1.76/1.93  
% 1.76/1.93  Length of proof is 3.  Level of proof is 2.
% 1.76/1.93  
% 1.76/1.93  ---------------- PROOF ----------------
% 1.76/1.93  % SZS status Theorem
% 1.76/1.93  % SZS output start Refutation
% See solution above
% 1.76/1.93  ------------ end of proof -------------
% 1.76/1.93  
% 1.76/1.93  
% 1.76/1.93  Search stopped by max_proofs option.
% 1.76/1.93  
% 1.76/1.93  
% 1.76/1.93  Search stopped by max_proofs option.
% 1.76/1.93  
% 1.76/1.93  ============ end of search ============
% 1.76/1.93  
% 1.76/1.93  -------------- statistics -------------
% 1.76/1.93  clauses given                  5
% 1.76/1.93  clauses generated             55
% 1.76/1.93  clauses kept                  57
% 1.76/1.93  clauses forward subsumed      25
% 1.76/1.93  clauses back subsumed          3
% 1.76/1.93  Kbytes malloced              976
% 1.76/1.93  
% 1.76/1.93  ----------- times (seconds) -----------
% 1.76/1.93  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.76/1.93  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.76/1.93  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.76/1.93  
% 1.76/1.93  That finishes the proof of the theorem.
% 1.76/1.93  
% 1.76/1.93  Process 4623 finished Wed Jul 27 10:46:50 2022
% 1.76/1.93  Otter interrupted
% 1.76/1.93  PROOF FOUND
%------------------------------------------------------------------------------